Multiplayer should improve Elite not restrict it. Groups and open play would profit if the galaxy was generally more dangerous. Merchants and travellers used to band together for security.
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All the missions are single stage, as has been mentioned if there was a proportion of quest missions aimed at groups it would help. The quest missions, when accomplished, could lead into local community goals.
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Elite also lacks unique titles and honours which could enhance open play. As an example, how about the 'Presence of Nemesis?'
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The killer of the current 'Presence of Nemesis' is awarded the title. Nemesis must always exist in open play, if the player with the title goes into a no-fire zone, docks, offlines or otherwise exits open play, an AI Nemesis spawns. If the AI Nemesis is killed the killer becomes Nemesis, otherwise the current Nemesis may resume upon return. If Nemesis invites a player to a wing that player is the new Nemesis. There are no effects associated with holding the title, other than it being shown on-screen.
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All it would cost it some code tracking Nemesis and enough screen space to state 'Presence of Nemesis.' Helen of Troy was just a good-looking girl, yet she managed to start an epic scrap?